Polishing tool, polishing method and polishing apparatus

ABSTRACT

A polishing tool includes a polishing surface having a spherical zone shape and having a plurality of non-contact portions provided from an inner edge to an outer edge of the polishing surface so as not to contact with a workpiece. The plurality of non-contact portions is a plurality of grooves whose widths in a circumferential direction increase from the inner edge toward the outer edge. A polishing method using the polishing tool includes: rotating the polishing tool about the central axis of rotation; and simultaneously with rotating the polishing tool, swinging relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby polishing the workpiece.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation of PCT international application Ser.No. PCT/JP2015/063206, filed on May 7, 2015 which designates the UnitedStates, incorporated herein by reference, and which claims the benefitof priority from Japanese Patent Application No. 2014-119901, filed onJun. 10, 2014, incorporated herein by reference.

BACKGROUND

1. Technical Field

The disclosure relates to a polishing tool, a polishing method, and apolishing apparatus for surface finishing of optical elements such aslenses.

2. Related Art

Typically, for surface finishing of optical elements such as lenses,prisms, and mirrors, a polishing tool and a workpiece are made to slidealong each other so that the object is polished by abrasive grains forpolishing present at the interface. A polishing tool is fabricated bymaking pellets of fixed abrasive grains adhere to a base plate to make adesired curved surface with the fixed abrasive grains or adheringpolishing sheets made of polyurethane formed in a desired curved surfaceonto a base plate.

In recent years, the have been demands for optical elements with highshape accuracy and with no surface irregularity. For example, JP2006-136959 A discloses a polishing tool in which the distances from therotary axis of the polishing tool to the outer circumferential shape ofthe work surface on which a workpiece is polished are not equal alongthe rotational direction, which is a polishing tool that achieves highshape accuracy by using an existing polishing apparatus without anychange.

SUMMARY

In some embodiments, a polishing tool includes a polishing surfacehaving a spherical zone shape and having a plurality of non-contactportions provided from an inner edge to an outer edge of the polishingsurface so as not to contact with a workpiece. The plurality ofnon-contact portions is a plurality of grooves whose widths in acircumferential direction increase from the inner edge toward the outeredge.

In some embodiments, a polishing method using the polishing toolincludes: rotating the polishing tool about the central axis ofrotation; and simultaneously with rotating the polishing tool, swingingrelatively at least one of the workpiece and the polishing tool with apredetermined swing width, around a position where a line passingthrough a center of the workpiece and intersecting with the central axisof rotation passes through a center in a width direction of a sphericalzone of the polishing surface, thereby polishing the workpiece.

In some embodiments, a polishing apparatus includes: the polishing tool;a pressure applying unit configured to bring the workpiece into contactwith the polishing surface of the polishing tool, thereby to applypressure to the workpiece; a rotating unit configured to rotate thepolishing tool about the central axis of rotation; and a swinging unitconfigured to swing relatively at least one of the workpiece and thepolishing tool with a predetermined swing width, around a position wherea line passing through a center of the workpiece and intersecting withthe central axis of rotation passes through a center in a widthdirection of a spherical zone of the polishing surface, thereby topolish the workpiece.

In some embodiments, a polishing tool includes a polishing surfacehaving a spherical zone shape and having a plurality of non-contactportions provided from an inner edge to an outer edge of the polishingsurface so as not to contact with a workpiece. The plurality ofnon-contact portions is formed by a plurality of holes, and a densityper unit area of the plurality of holes increases from the inner edgetoward the outer edge.

In some embodiments, a polishing method using the polishing toolincludes: rotating the polishing tool about the central axis ofrotation; and simultaneously with rotating the polishing tool, swingingrelatively at least one of the workpiece and the polishing tool with apredetermined swing width, around a position where a line passingthrough a center of the workpiece and intersecting with the central axisof rotation passes through a center in a width direction of a sphericalzone of the polishing surface, thereby polishing the workpiece.

In some embodiments, a polishing apparatus includes: the polishing tool;a pressure applying unit configured to bring the workpiece into contactwith the polishing surface of the polishing tool, thereby to applypressure to the workpiece; a rotating unit configured to rotate thepolishing tool about the central axis of rotation; and a swinging unitconfigured to swing relatively at least one of the workpiece and thepolishing tool with a predetermined swing width, around a position wherea line passing through a center of the workpiece and intersecting withthe central axis of rotation passes through a center in a widthdirection of a spherical zone of the polishing surface, thereby topolish the workpiece.

The above and other features, advantages and technical and industrialsignificance of this invention will be better understood by reading thefollowing detailed description of presently preferred embodiments of theinvention, when considered in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic view illustrating a configuration of a polishingapparatus according to a first embodiment of the present invention;

FIG. 2 is a cross-sectional view of a polishing tool used in FIG. 1;

FIG. 3 is a top view of the polishing tool of FIG. 2;

FIG. 4 is a schematic view for explaining a method for polishing a lensusing the polishing apparatus illustrated in FIG. 1;

FIG. 5 is a schematic view for explaining the method for polishing alens using the polishing apparatus illustrated in FIG. 1;

FIG. 6 is a top view of a polishing tool according to a firstmodification of the present invention;

FIG. 7 is a top view of a polishing tool according to a secondmodification of the present invention;

FIG. 8 is a top view of a polishing tool according to a thirdmodification of the present invention;

FIG. 9 is a top view of a polishing tool according to a fourthmodification of the present invention;

FIG. 10 is a top view of a polishing tool according to a fifthmodification of the present invention;

FIG. 11 is a top view of a polishing tool according to a sixthmodification of the present invention; and

FIG. 12 is a diagram explaining a structure of a polishing surfaceformed on a polishing tool according to a second embodiment.

DETAILED DESCRIPTION

Embodiments of the present invention will now be described withreference to the drawings. The present invention is not limited to theembodiments. The same reference signs are used to designate the sameelements throughout the drawings. The drawings are schematic, and therelative sizes and ratios of elements may be different from the actualsizes and ratios. The relative sizes and ratios of the elements may bedifferent between the drawings.

First Embodiment

FIG. 1 is a schematic view illustrating a configuration of a polishingapparatus according to a first embodiment of the present invention. FIG.2 is a cross-sectional view of a polishing tool used in FIG. 1, and FIG.3 is a top view of the polishing tool of FIG. 2. A polishing apparatus100 according to the first embodiment includes a polishing tool 3, aholder 2 for bringing a lens 1 as a workpiece, into contact with apolishing surface 30 b of the polishing tool 3, a rotary motor 7 forrotating the polishing tool 3, and a swing motor 6 for swinging thepolishing tool 3.

As illustrated in FIGS. 2 and 3, the polishing tool 3 has a base plate30 a, and the polishing surface 30 b of a spherical zone shape. Thespherical zone shape refers to a shape of a surface of a sphericalsegment remaining between two parallel planes when a sphere is cut bythe two parallel planes. An opening 30 c is formed on a projection planeon which the polishing surface 30 b is projected and which isperpendicular to a central axis of rotation O of the polishing surface,on the inner edge side of the polishing surface 30 b, where the opening30 c and the outer edge of the polishing surface 30 b are concentricabout the central axis of rotation O. The base plate 30 a is formed tohave a predetermined radius of curvature, which is substantially aninverse of the shape of the lens 1 as a workpiece.

As illustrated in FIG. 3, the polishing surface 30 b includes effectivepolishing portions 30 d that come into contact with the lens 1 andpractically polish the lens 1, and non-contact portions 30 e that do notcome into contact with the lens 1 and do not directly contribute topolishing the lens 1. In the first embodiment, 12 polishing sheetshaving a substantially rectangular shape are attached to part of thesurface of the base plate 30 a to form the effective polishing portions30 d and the non-contact portions 30 e. The effective polishing portions30 d are regions of the polishing surface 30 b to which the polishingsheets are attached. The effective polishing portions 30 d are shaded inFIG. 3.

The non-contact portions 30 e are regions of the polishing surface 30 bwhere the polishing sheets are not attached so as to expose the surfaceof the base plate 30 a, and form grooves recessed from the effectivepolishing portions 30 d. Hereinafter, the non-contact portions 30 e willalso be referred to as grooves 30 e. In the first embodiment, thegrooves 30 e are substantially fan-shaped on the projection plane onwhich the polishing surface 30 b is projected and which is perpendicularto the central axis of rotation O. FIG. 2 is a cross-section of thepolishing tool 3 along the groove 30 e.

As illustrated in FIG. 1, the polishing tool 3 is connected to an upperend of a tool shaft 4, and the tool shaft 4 is integrally attached to aspindle 5. The spindle 5 is connected to the rotary motor 7, and therotary motor 7 is fixed to a lower shaft base plate 14 that rotatablysupports the spindle 5. The rotary motor 7 is a rotating unit forrotating the polishing tool 3 about the axis of the rotary shaft underthe control of a controller for controlling the polishing apparatus 100.The lower shaft base plate 14 has an upper portion extending through aswing member 9, and is mounted in such a manner that the outer surfaceof the upper portion is integrated with the swing member 9. The swingmotor 6 is fixed to the lower shaft base plate 14 in such a manner thatthe rotary axis of the swing motor 6 is perpendicular to that of therotary motor 7. The swing motor 6 swings the swing member 9 under thecontrol of the controller. The rotating speed and the number orrotations of the swing motor 6 can be freely controlled. The swing motor6 and the swing member 9 constitute a swinging unit.

The swing member 9 has a boat shape with a lower surface supported by aswing member receiving portion 10 fixed to a main body of the polishingapparatus 100. The swing member receiving portion 10 has a surfacefacing the swing member 9 having a concave shape corresponding to thebottom surface of the boat shape to swingably support the swing member9, and forms an opening portion for eliminating interference with thelower shaft base plate 14 while the swing member 9 swings.

A gear 6 a is attached to a drive shaft of the swing motor 6, and mesheswith an arc-shaped guide 8. The guide 8 is fixed to a polishingapparatus main body 20, so that the gear 6 a is rotated by the swingmotor 6 while moving along the guide 8, which makes the lower shaft baseplate 14 swing and makes the swing member 9, the polishing tool 3, andso on swing in a reciprocating manner.

The lens 1 held by attachment to an attachment plate 12 is placed abovethe polishing tool 3. The lens 1 has a lens surface 1 a to be processedhaving a convex spherical shape and facing the polishing tool 3, and theattachment plate 12 is held in the inside of the holder 2, which is aholding tool, so that the lens 1 is rotatably supported relative to theholder 2. Although the attachment plate 12 and the holder 2 areillustrated in a separated state in FIG. 1, the attachment plate 12 andthe holder 2 are assembled with the polishing apparatus main body 20therebetween. The holder 2 is coupled to a lower end side of a workshaft 11, and the work shaft 11 is moved vertically by a rod of apressure applying air cylinder 16 coupled to an upper end of the workshaft 11. In addition, a polishing solution supplying part 13 forsupplying polishing solution to the polishing surface 30 b is providednear the polishing tool 3.

The pressure applying air cylinder 16 is attached to a first attachmentplate 19 a fixed to a top surface of a back plate 19, and makes the lenssurface 1 a to be processed in contact with the polishing surface 30 bof the polishing tool 3 to apply pressure thereto during processing ofthe lens 1 after the lens 1 is moved downward toward the polishing tool3 under the control of the controller for controlling the polishingapparatus 100. The first attachment plate 19 a and the back plate 19 donot move vertically during processing of the lens 1.

The central axis of the work shaft 11 is positioned on an axis passingthrough the center of curvature of the polishing surface 30 b of thepolishing tool 3. A coarse adjustment air cylinder 18 is fixed to thepolishing apparatus main body 20, and has a rod coupled to a secondattachment plate 19 b fixed to a front surface of the back plate 19. Thecoarse adjustment air cylinder 18 vertically moves the back plate 19,the pressure applying air cylinder 16, and the like. When the back plate19, the pressure applying air cylinder 16, and the like are moveddownward, the work shaft 11 and the holder 2 pass through a hole 20 aformed in the polishing apparatus main body 20 to make the lens 1 facethe polishing tool 3. In FIG. 1, a state in which the work shaft 11 andholder 2 have not passed through the hole 20 a is illustrated. Thepressure applying air cylinder 16 applies pressure in a direction inwhich the holder 2 and the like supporting the lens 1 are moveddownward, that is, vertically downward.

Linear scales 17, which are measuring devices or position detectors usedas a pair on a movable side and a fixed side, are disposed on the workshaft 11 and the back plate 19 below the pressure applying air cylinder16. The linear scale 17 detects the amount by which the work shaft 11 ismoved by the pressure applying air cylinder 16, and displays themovement amount on a display or the like. In addition, a stopper 15capable of adjusting vertical position is fixed to the back plate 19.The stopper 15 is disposed so that, when the back plate 19, that is, theentire upper part of the holder 2 and the like supporting the lens 1 viathe back plate 19 is moved downward by the coarse adjustment aircylinder 18, the stopper 15 on the back plate 19 side abuts a stopper 21on the main body side fixed to the polishing apparatus main body 20.

Next, a method for polishing the lens 1 using the polishing apparatus100 according to the first embodiment will be explained. FIGS. 4 and 5are schematic views for explaining the method for polishing the lens 1using the polishing apparatus 100 according to the first embodiment.

In the first embodiment, polishing of the lens 1 with the polishingapparatus 100 is performed by swinging the polishing tool 3 around aswing center position illustrated in FIG. 4 with a certain amplitudewhile rotating the polishing tool 3 about a central axis of rotation Oby the rotary motor 7. The swing center position is a position where aline L passing through the center C of the lens 1 and intersecting withthe central axis of rotation O passes through the center B in the widthdirection of the spherical zone of the polishing surface 30 b asillustrated in FIG. 4. The lens 1 is rotated with the polishing tool 3in the same direction as the rotating direction by a frictional forcecaused by the rotation. The lens 1 is polished by the polishing surface30 b having the spherical zone shape where the circumferential speed atthe inner diameter D_(in), which is an inner edge side of the polishingsurface 30 b, is different from the circumferential speed at an outerdiameter D_(out), which is an outer edge side thereof. The applicant hasfound that, when the difference in the circumferential speed between theinner edge side and the outer edge side of the polishing surface 30 b islarge, a surface irregularity such as a central rise where the centralportion of the processed lens surface 1 a of the lens 1 is higher thanthat of a reference lens as a reference, or a central drop where thecentral portion is lower than that of the reference lens occurs, whichlowers the surface accuracy.

Thus, in the first embodiment, as illustrated in FIGS. 4 and 5, thepolishing surface 30 b has a spherical zone shape so that acircumferential speed ratio Vo/Vi of the circumferential speed Vo on theouter edge side to the circumferential speed Vi on the inner edge sideis smaller than that of a conventional polishing tool, that is, apolishing tool having a spherical surface without the opening 30 c.Furthermore, as illustrated in FIG. 3, the polishing surface 30 b hasthe grooves 30 e such that an effective circumferential speed ratio isapproximately constant regardless of the diameter, at an arbitrarydiameter on the projection plane on which the polishing surface 30 b isprojected and which is perpendicular to the central axis of rotation O.The effective circumferential speed ratio refers to a ratio between alength per unit time where the lens 1 is in contact with the effectivepolishing portions 30 d at an arbitrary diameter of the polishingsurface 30 b (hereinafter referred to as an effective circumferentialspeed) and the effective circumferential speed at the inner edge of thepolishing surface 30 b. The effective circumferential speed ratiocorresponds to a ratio of an effective circumferential length at anarbitrary diameter of the polishing surface 30 b to an effectivecircumferential length at the inner edge of the polishing surface 30 b.The effective circumferential length refers to a total of thecircumferential lengths of the effective polishing portions 30 d of thepolishing surface 30 b.

Specifically, the effective circumferential speed ratio α at the outeredge of the polishing surface 30 b is 6.0 or smaller, preferably 4.0 orsmaller, and more preferably 3.0 or smaller. The effectivecircumferential speed ratio α is most preferably 1.0, and may be smallerthan 1.0. Preferably, the effective circumferential speed ratio α may be0.7 or higher. Furthermore, a tolerance range of the effectivecircumferential speed ratio α is preferably within ±30%, and morepreferably ±10%, in view of the accuracy of the finishing shape of thepolishing surface 30 b, the posture stability of the lens 1 duringprocessing of the lens 1, the surface accuracy after processing, and thelike.

If the effective circumferential speed ratio α between the inner edgeand the outer edge of the polishing surface 30 b is α≠1.0, the effectivecircumferential speed ratio β at an arbitrary diameter preferablychanges as linearly as possible from the inner edge toward the outeredge. If the effective circumferential speed ratio α is α=1, it ispreferable that the effective circumferential speed ratio β be also 1,and in this case, the tolerance range of the effective circumferentialspeed ratio β is also preferably within ±30%, and more preferably within±10%.

The effective circumferential speed ratio α at the outer edge of thepolishing surface 30 b is given by the following expression (1) usingthe effective circumferential length L_(in) at the inner edge and theeffective circumferential length L_(out) at the outer edge of thepolishing surface 30 b.

α=L _(out) /L _(in)  (1)

In addition, the effective circumferential length L_(in) at the inneredge is given by the following expression (2) using the groove width gof the grooves 30 e and the number m of the grooves 30 e.

$\begin{matrix}{{Li}_{n} = {{\pi \times D_{i\; n}} - {\frac{D_{i\; n} \times m}{2} \times {\arcsin ( \frac{g}{D^{i\; n}} )}}}} & (2)\end{matrix}$

When the effective circumferential length L_(out) at the outer edge andthe effective circumferential length L_(in) at the inner edge aredifferent from each other, that is, when the effective circumferentialspeed ratio α is α≠1.0, the effective circumferential speed ratio β ischanged linearly from the inner edge toward the outer edge in the radialdirection of the polishing surface 30 b as described above. In thiscase, the effective circumferential speed ratio β(D) at an arbitrarydiameter D (D_(in)<D<D_(out)) is given by the following expression (3)using the inner diameter D_(in) and the outer diameter D_(out) ofpolishing surface 30 b.

$\begin{matrix}{{\beta (D)} = {\frac{( {\alpha - 1} ) \times ( {D - D_{i\; n}} )}{D_{out} - D_{i\; n}} + 1}} & (3)\end{matrix}$

Here, a line passing through the center in the circumferential directionof an arbitrary groove 30 e at the inner edge is referred to as areference line L1, and a line or a curve passing through the center inthe circumferential direction of another groove 30 e other than thearbitrary groove 30 e is referred to as a center line L2. In addition,an angle between the reference line L1 and a line for connecting a pointP1 where the center line L2 passes through a circumference at thearbitrary diameter D and the central axis of rotation O of the polishingsurface 30 b, is denoted by θ. The line connecting the point P1 and thecentral axis of rotation O corresponds to the center line L2 itself inFIG. 3.

The angle θ is given by the following expression (4).

$\begin{matrix}{{\theta = {{n \times \frac{2\pi}{m}} + {f(D)}}}( {{n = 1},2,\ldots \mspace{14mu},m} )} & (4)\end{matrix}$

In the expression (4), a function f(D) is a function expressing theangle between the center line L2 and a radius passing through the P1. Inthe case of FIG. 3, f(D)=0, and the center line L2 is a line passingthrough the central axis of rotation O. When the function f(D) is variedwith the diameter D, the center line L2 is an arbitrary curve.

In the groove 30 e including the center line L2, an angle φ between aradius passing through each of end points P2 and P3 on the circumferencewith the diameter D and the reference line L1 is given by the followingexpression (5).

φ=θ±ω  (5)

The angle ω in the expression (5) is a half-angle of the central angleof a sector with an arc of the groove 30 e on the circumference with thediameter D, that is, the central angle of an arc connecting the pointsP1 and P2 or an arc connecting the points P1 and P3, and is given by thefollowing expression (6).

$\begin{matrix}{\omega = {\frac{\pi}{m} - \frac{\beta \times L_{i\; n}}{m \times D}}} & (6)\end{matrix}$

With the expressions (1) to (6), the shape of the grooves 30 e on thepolishing surface 30 b can be designed in such a manner that theparameters including the inner diameter D_(in) and the outer diameterD_(out) of the polishing surface 30 b, the number m of the grooves 30 e,the groove width g at the inner edge, the effective circumferentialspeed ratio α at the outer edge, and the function f(D) are set, andcoordinates of the end points P2 and P3 are sequentially calculated. Thepolishing surface 30 b illustrated in FIG. 3 is an example of a designwith the inner diameter D_(in)=18 cm, the outer diameter D_(out)=36 cm,the number m of the grooves m=12, the groove width g at the inner edgeg=1 cm, the effective circumferential speed ratio α=1, and the functionf(D)=0.

As described above, in the polishing tool according to the firstembodiment, the shape of the polishing surface is a spherical zone shapeso that the difference in the circumferential length between the inneredge and the outer is made small, and grooves that are not brought intocontact with a workpiece are formed on the polishing surface. As aresult, the effective circumferential length ratio at the outer edge ofthe polishing surface can be made smaller, and variation in theeffective circumferential length ratio can be reduced regardless of thediameter. Consequently, occurrence of a surface irregularity on thepolishing surface can be reduced, and the surface accuracy of aworkpiece can be increased.

Although the effective polishing portions 30 d and the grooves 30 e areformed by attaching polishing sheets shaped into a predetermined shapeonto the surface of the base plate 30 a in the first embodiment, thegrooves 30 e may alternatively be formed by fixing abrasive grains forpolishing on the base plate with resin or the like, forming thepolishing surface 30 b of a spherical zone shape having a desired radiusof curvature by cutting, and then cutting out regions of the polishingsurface 30 b other than the effective polishing portions 30 d.

Furthermore, although the holder 2 is not particularly moved but onlythe lens 1 is pressed against the polishing tool 3 and the polishingtool 3 side is rotated and swung during polishing of the lens 1 in thefirst embodiment, either side may be moved as long as the lens 1 and thepolishing tool 3 can be relatively moved. For example, the polishingtool 3 may be rotated and the lens 1 and the holder 2 side may be swung.Alternatively, the polishing tool 3 may be rotated and both the lens 1,the holder 2 and the polishing tool 3 may be swung relatively.

First Modification

Next, a first modification of the first embodiment will be described.FIG. 6 is a top view of a polishing tool according to the firstmodification. A polishing surface 31 illustrated in FIG. 6 is an exampleof a design of effective polishing portions 31 a and grooves 31 b withthe parameters in the expressions (1) to (6) being: the inner diameterD_(in)=18 cm, the outer diameter D_(out)=36 cm, the number m of groovesm=6, the groove width g at the inner edge g=0 cm, the effectivecircumferential speed ratio α=1, and the function f(D)=0. The grooves 31b are substantially fan-shaped on the projection plane obtained byprojecting the polishing surface 31 having the spherical zone shape ontothe plane perpendicular to the central axis of rotation O of thepolishing surface 31. The effective polishing portions 31 a are shadedin FIG. 6.

Although the number of grooves 31 b formed on the polishing surface 31is not limited, the lens 1 needs to be prevented from falling into thegroove 31 b during processing of the lens 1 in the polishing apparatus100 illustrated in FIG. 1. Thus, when the center axis C of the lens 1 isat a position at an end of the groove 31 b or on the groove 31 b, arequired condition is that part of a sphere (the hatched part, forexample) of the lens 1 defined by an arbitrary line passing through thecenter axis C of the lens 1 remains on an effective polishing portion 31a. To meet the condition, for making ends of the grooves 31 b on aprojection plane of the polishing surface 31 linear (that is, f(D)=0),the number of grooves may be at least six.

Even if the groove width g at the inner edge is zero, a gap for aprocessing tool may actually be present between adjacent grooves 31 b atthe inner edge of the polishing surface 31.

Second Modification

Next, a second modification of the first embodiment will be described.FIG. 7 is a top view of a polishing tool according to the secondmodification. A polishing surface 32 illustrated in FIG. 7 is an exampleof a design of effective polishing portions 32 a and grooves 32 b withthe parameters in the expressions (1) to (6) being: the inner diameterD_(in)=18 cm, the outer diameter D_(out)=36 cm, the number m of groovesm=12, the groove width g at the inner edge g=0 cm, the effectivecircumferential speed ratio α=1, and the function f(D)=0. The grooves 32b are substantially fan-shaped on the projection plane on which thepolishing surface 32 having the spherical zone shape is projected andwhich is perpendicular to the central axis of rotation O of thepolishing surface 32. The effective polishing portions 32 a are shadedin FIG. 7.

Third Modification

Next, a third modification of the first embodiment will be described.FIG. 8 is a top view of a polishing tool according to the thirdmodification. A polishing surface 33 illustrated in FIG. 8 includeseffective polishing portions 33 a, grooves 33 b extending in thecircumferential direction, and grooves 33 c formed in the radialdirection. The polishing surface 33 is obtained by forming the grooves33 c using the same parameters as those of the second modification, andforming the grooves 33 b in the circumferential direction so that theeffective polishing portions 33 a forming an alternate strip pattern inadjacent regions other than the grooves 33 c are left. The effectivepolishing portions 33 a are shaded in FIG. 8.

Formation of such grooves 33 b facilitates flow out of slurry duringprocessing of the lens 1. Furthermore, since the grooves 33 b are formedto have an alternative strip pattern in adjacent regions on the samecircumference, the effective polishing portions 33 a remaining on thecircumference at an arbitrary diameter, that is, the effectivecircumferential length, can be made uniform regardless of the diameter.Furthermore, as a result of formation of the grooves 33 b, the lens 1 isprevented from falling into the groove 33 b or 33 c during processing ofthe lens 1 while increasing the total area of the grooves 33 b and 33 con the polishing surface 33.

Fourth Modification

Next, a fourth modification of the first embodiment will be described.FIG. 9 is a top view of a polishing tool according to the fourthmodification. A polishing surface 34 illustrated in FIG. 9 is designedto have effective polishing portions 34 a and grooves 34 b with theparameters in the expressions (1) to (6) being as follows: the innerdiameter D_(in)=18 cm; the outer diameter D_(out)=36 cm; the number m ofthe grooves m=12; the groove width g at the inner edge g=0 cm; theeffective circumferential speed ratio α=1; and the functionf(D)=arccos(k×D). The coefficient k is designed to be constant such thatf(D)=0 when D=18 cm and f(D)=60° when D=36 cm. With such a functionf(D), spiral grooves 34 b each having a straight center line L2 in thecircumferential direction are formed. The effective polishing portions34 a are shaded in FIG. 9.

Similarly to the third modification, grooves extending in thecircumferential direction may be provided in the effective polishingportions 34 a of the fourth modification.

Fifth Modification

Next, a fifth modification of the first embodiment will be described.FIG. 10 is a top view of a polishing tool according to the fifthmodification. A polishing surface 35 illustrated in FIG. 10 is designedto have effective polishing portions 35 a and grooves 35 b with theparameters in the expressions (1) to (6) being as follows: the innerdiameter D_(in)=18 cm; the outer diameter D_(out)=36 cm; the number m ofthe grooves m=12; the groove width g at the inner edge g=0 cm; theeffective circumferential speed ratio α=1; and the functionf(D)=k×(D−18). The coefficient k is designed to be constant such thatf(D)=0 when D=18 cm and f(D)=36° when D=36 cm. With such a functionf(D), spiral grooves 35 b each having an arc-like center line L2 in thecircumferential direction are formed. The effective polishing portions35 a are shaded in FIG. 10.

Similarly to the third modification, grooves extending in thecircumferential direction may also be provided in the effectivepolishing portions 35 a of the fifth modification.

Sixth Modification

Next, a sixth modification of the first embodiment will be described.FIG. 11 is a top view of a polishing tool according to the sixthmodification. A polishing surface 36 illustrated in FIG. 11 is designedto have effective polishing portions 36 a and grooves 36 b with theparameters in the (1) to (6) being as follows: the inner diameterD_(in)=18 cm; the outer diameter D_(out)=36 cm; the number m of thegrooves m=12; the groove width g at the inner edge g=0 cm; the effectivecircumferential speed ratio α=1; and the function f(D)=j×sin(k×D). Thecoefficient k is designed to be constant such that f(D)=0 when D=18 cmand 36 cm, and a single inflection point is present in a range of 18cm<D<36 cm. In addition, the coefficient j is designed to be constantsuch that f(D) 14.3 at the inflection point. As in the sixthmodification, the center line L2 in the circumferential direction of thegroove 36 b is not limited to a straight line or an arc-like line, butmay be any curve having an inflection point. The effective polishingportions 36 a are shaded in FIG. 11.

Similarly to the third modification, grooves extending in thecircumferential direction may also be provided in the effectivepolishing portions 36 a of the sixth modification.

Second Embodiment

Next, a second embodiment of the present invention will be described.FIG. 12 is a diagram explaining a structure of a polishing surfaceformed on a polishing tool according to the second embodiment. Thepolishing tool according to the second embodiment has a polishingsurface 37 illustrated in (a) of FIG. 12. The polishing surface 37 has aspherical zone shape, and an opening 38 is formed on a projection planeon which the polishing surface 37 is projected and which isperpendicular to a central axis of rotation O of the polishing surface37 on the inner side of the polishing surface 37, where the opening 38and the outer edge of the polishing surface 37 are concentric about thecentral axis of rotation O. The structure of the polishing tool and thestructure of the whole polishing apparatus according to the secondembodiment other than the polishing surface 37 are the same as those ofthe first embodiment illustrated in FIGS. 1 and 2.

The polishing surface 37 includes effective polishing portions 37 a thatcome into contact with the lens 1 and practically polish the lens 1, andnon-contact portions 37 b that do not come into contact with the lens 1and do not directly contribute to polishing the lens 1. The effectivepolishing portions 37 a are formed by attaching polishing sheets, whichare obtained by fixing abrasive grains onto the surfaces of viscoelasticsheets made of polyurethane or the like, onto the base plate 30 aillustrated in FIG. 2. The effective polishing portions 37 a are shadedin FIG. 12.

In contrast, the respective non-contact portions 37 b are hole portionsformed in the polishing sheets where the surface of the base plate 30 ais exposed. The non-contact portions 37 b have a predetermined shapesuch as a circular shape, a rectangular shape, a polygonal shape, or astar-like shape. One non-contact portion 37 b may be continuous withanother adjacent non-contact portion 37 b or may be separate from anadjacent non-contact portion 37 b.

The non-contact portions 37 b are formed so that the hole density isincreased from the inner edge side toward the outer edge side of thepolishing surface 37. (b) in FIG. 12 is a graph showing a distributionof the hole density in the non-contact portions 37 b in the radialdirection (x direction) of the polishing surface 37. In the secondembodiment, the non-contact portions 37 b are arranged so that the holedensity increases approximately linearly from the inner edge side towardthe outer edge side.

As a result of forming the non-contact portions 37 b to achieve theabove-described hole density, the effective circumferential speed ratioat the outer edge of the polishing surface 37 is reduced, and variationin the effective circumferential speed ratio at an arbitrary diameter isreduced. Consequently, occurrence of a surface irregularity on thepolishing surface is reduced and the surface accuracy of a workpieceincreased.

In the second embodiment, instead of adhering polishing sheets havingholes formed therein onto the base plate, the non-contact portions 37 bmay alternatively be formed by fixing abrasive grains for polishing onthe base plate with resin or the like, forming the polishing surface 37of a spherical zone shape having a desired radius of curvature bycutting, and then performing cutting out on the polishing surface 37.

According to some embodiments, it is possible to improve a surfaceaccuracy of a workpiece while utilizing an existing apparatus withoutintroducing a new control device or the like.

The first and second embodiments and the modifications described aboveare only examples for carrying out the present invention, and thepresent invention is not limited to these embodiments and modification.Furthermore, in the present invention, more than one element disclosedin the first and second embodiments and the modifications may becombined where appropriate to constitute various aspects of the presentinvention. The present invention can be modified in various mannersdepending on specifications or the like, and various other embodimentscan be present within the scope of the present invention.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalents.

What is claimed is:
 1. A polishing tool comprising: a polishing surfacehaving a spherical zone shape and having a plurality of non-contactportions provided from an inner edge to an outer edge of the polishingsurface so as not to contact with a workpiece, wherein the plurality ofnon-contact portions is a plurality of grooves whose widths in acircumferential direction increase from the inner edge toward the outeredge.
 2. The polishing tool according to claim 1, wherein the pluralityof grooves is provided radially from the inner edge toward the outeredge.
 3. The polishing tool according to claim 1, wherein the pluralityof grooves forms a spiral pattern from the inner edge toward the outeredge.
 4. The polishing tool according to claim 2, wherein the polishingsurface further has a plurality of second grooves extending in thecircumferential direction of the polishing surface in regions of thepolishing surface excluding the plurality of grooves.
 5. The polishingtool according to claim 3, wherein the polishing surface further has aplurality of second grooves extending in the circumferential directionof the polishing surface in regions of the polishing surface excludingthe plurality of grooves.
 6. The polishing tool according to claim 4,wherein the plurality of second grooves is provided in every otherregion in the circumferential direction.
 7. The polishing tool accordingto claim 5, wherein the plurality of second grooves is provided in everyother region in the circumferential direction.
 8. The polishing toolaccording to claim 1, wherein on a projection plane on which thepolishing surface is projected and which is perpendicular to a centralaxis of rotation of the polishing surface: an effective circumferentiallength of the polishing surface is defined as a circumferential lengthat an arbitrary diameter by removing the plurality of non-contactportions; and if the effective circumferential length at the outer edgeis different from the effective circumferential length at the inneredge, the effective circumferential length at the arbitrary diameterlinearly changes from the inner edge toward the outer edge.
 9. Apolishing method using the polishing tool according to claim 1, themethod comprising: rotating the polishing tool about the central axis ofrotation; and simultaneously with rotating the polishing tool, swingingrelatively at least one of the workpiece and the polishing tool with apredetermined swing width, around a position where a line passingthrough a center of the workpiece and intersecting with the central axisof rotation passes through a center in a width direction of a sphericalzone of the polishing surface, thereby polishing the workpiece.
 10. Apolishing apparatus comprising: the polishing tool according to claim 1;a pressure applying unit configured to bring the workpiece into contactwith the polishing surface of the polishing tool, thereby to applypressure to the workpiece; a rotating unit configured to rotate thepolishing tool about the central axis of rotation; and a swinging unitconfigured to swing relatively at least one of the workpiece and thepolishing tool with a predetermined swing width, around a position wherea line passing through a center of the workpiece and intersecting withthe central axis of rotation passes through a center in a widthdirection of a spherical zone of the polishing surface, thereby topolish the workpiece.
 11. A polishing tool comprising: a polishingsurface having a spherical zone shape and having a plurality ofnon-contact portions provided from an inner edge to an outer edge of thepolishing surface so as not to contact with a workpiece, wherein theplurality of non-contact portions is formed by a plurality of holes, anda density per unit area of the plurality of holes increases from theinner edge toward the outer edge.
 12. The polishing tool according toclaim 11, wherein on a projection plane on which the polishing surfaceis projected and which is perpendicular to a central axis of rotation ofthe polishing surface: an effective circumferential length of thepolishing surface is defined as a circumferential length at an arbitrarydiameter by removing the plurality of non-contact portions; and if theeffective circumferential length at the outer edge is different from theeffective circumferential length at the inner edge, the effectivecircumferential length at the arbitrary diameter linearly changes fromthe inner edge toward the outer edge.
 13. A polishing method using thepolishing tool according to claim 11, the method comprising: rotatingthe polishing tool about the central axis of rotation; andsimultaneously with rotating the polishing tool, swinging relatively atleast one of the workpiece and the polishing tool with a predeterminedswing width, around a position where a line passing through a center ofthe workpiece and intersecting with the central axis of rotation passesthrough a center in a width direction of a spherical zone of thepolishing surface, thereby polishing the workpiece.
 14. A polishingapparatus comprising: the polishing tool according to claim 11; apressure applying unit configured to bring the workpiece into contactwith the polishing surface of the polishing tool, thereby to applypressure to the workpiece; a rotating unit configured to rotate thepolishing tool about the central axis of rotation; and a swinging unitconfigured to swing relatively at least one of the workpiece and thepolishing tool with a predetermined swing width, around a position wherea line passing through a center of the workpiece and intersecting withthe central axis of rotation passes through a center in a widthdirection of a spherical zone of the polishing surface, thereby topolish the workpiece.